Seems like I cannot apply the transformation correctly.
I tried ∂X/∂t=(∂X/∂τ)*(∂τ/∂t), calculating (∂τ/∂t) from the transformation formulae, then: ∂N/∂y=∂N/∂η and so on. But I guess it is not right. I think I have to somehow use that τ=τ(t,x) (assuming v=const), but I don't know how.
And I don't understand how and most importantly why do Y and Z appear in the equation for X?

I would be really grateful if anyone could give me a hint.
Thank you in advance.